1. Field of the Invention
The invention generally relates to the field of printing systems, and in particular, to methods and systems for linear processing in color conversion.
2. Statement of the Problem
In color printing, displaying, and reproduction, the term gamut represents the set of colors that a color-reproduction device is physically able to generate. Every device that displays or reproduces an image, such as a printer, monitor, scanner, or digital camera, may have its own unique color gamut. When an image is transferred from one device to another, the color gamut of each device is examined to closely match the color in the transferred image. That is, an attempt is made to closely match the color gamut of the image originating device in the device to which the image is being transferred so as to provide the most aesthetically pleasing color conversion. For example, the color gamut of a digital camera is generally greater than the color gamut of a printer. When color values of the digital camera color gamut are mapped to the color gamut of the printer, the conversion process generally requires intense analysis to ensure that the print quality is sufficiently high.
Adding to the complexity are the color spaces themselves. For example, perceptual color spaces, such as CIELab, are visualized as three dimensional color spaces, where every color that humans can see is uniquely located. Though the CIELab color space is a perceptual color space, it is not a perceptually uniform color space as the Euclidean distance in the space does not correspond to the perceptual distance. For example, the magnitude of the perceptual color difference generally depends upon the color location and the changing direction in chroma and hue. CIELab increasingly overstates the magnitudes of perceived chroma differences. The human visual system (HVS) is sensitive to the change of chroma in the neutral color area and insensitive to the change of the chroma in a highly saturated color area. The CIELab color space is also non-uniform regarding hue angle in that the thresholds of visual tolerances are a function of hue angle. If the non-uniformity of the CIELab color space in chroma and hue is examined from another perspective, CIELab colors have different characteristics at different locations. The change of these characteristics is generally continuous.
Most printers (i.e., toner and ink based printers) are able to produce only a limited numbers of gray levels. In order to produce continuous tone imagery that contains an infinite range of colors or grays, a reprographic technique called halftoning is applied to create the illusion of continuous tone images through the use of dot arrangements and dots of varying size. The combination of the printer halftone design and the specific toner/ink selection determine the number of colors that a printer is physically able to produce (i.e., the gamut).
Printer color conversions are generally performed between a device-dependent color space and a device-independent color space. For example, CMYK color patches whose values span the CMYK color space are first printed. The printed patches are then measured using a spectral photometer which determines the spectral reflectance of each patch under a standard illuminant. Software in the spectral photometer calculates the tristimulus values and converts these values to CIELab values. The CIELab values are floating point numbers. Color conversion lookup tables are generated using this set of data to convert color values of the CIELab space to the CMYK space. However, the relationship between CMYK color space and the CIELab color space is highly nonlinear due to the interactions of cyan, magenta, yellow, and black planes. The color conversions, therefore, generally require complex functions. Another complication to the printer color conversion regards the halftone design. Most halftone techniques are capable of creating color gray levels continuously but have an abrupt change between two adjacent levels. Thus, the color conversion between CMYK and CIELab may be continuous but not differentiable.
Moreover, certain CMYK values may be mapped to the same CIELab value. Since the range of CIELab color space is generally much larger than the range of the CMYK color space, there are no CMYK conversions for many CIELab values. Additionally, the CIELab to CMYK conversion has one degree of freedom such that one CIELab value may be mapped to several CMYK values. The inventor of the present application has discovered that radial basis functions (RBFs) are useful in such a color conversion process because, among other reasons, they are capable of approximating an unknown function from data. However, there remains a need to include error approximations in the numerical model(s) generated from the RBFs to ensure that the color conversion is accurate. Moreover, due to the complexity of the RBF computations, there exists a need to linearize the computations.